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Sibirsk. Mat. Zh., 2003, Volume 44, Number 4, Pages 772–778 (Mi smj1212)  

This article is cited in 8 scientific papers (total in 8 papers)

Subquadratic growth of the averaged Dehn function for free Abelian groups

E. G. Kukina, V. A. Roman'kov

Omsk State University

Abstract: For finite rank free abelian groups with the standard presentation, the averaged Dehn function is proved to be subquadratic.

Keywords: averaged Dehn function, isoperimetric function, free abelian group, plane cristallographic group, Cayley graph

Full text: PDF file (206 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2003, 44:4, 605–610

Bibliographic databases:

UDC: 517.55
Received: 23.04.2002

Citation: E. G. Kukina, V. A. Roman'kov, “Subquadratic growth of the averaged Dehn function for free Abelian groups”, Sibirsk. Mat. Zh., 44:4 (2003), 772–778; Siberian Math. J., 44:4 (2003), 605–610

Citation in format AMSBIB
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\by E.~G.~Kukina, V.~A.~Roman'kov
\paper Subquadratic growth of the averaged Dehn function for free Abelian groups
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 4
\pages 772--778
\mathnet{http://mi.mathnet.ru/smj1212}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2010125}
\zmath{https://zbmath.org/?q=an:1032.20029}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 4
\pages 605--610
\crossref{https://doi.org/10.1023/A:1024776205243}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184886500006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Roman'kov, “Subcubic growth of the averaged Dehn function for a class 2 nilpotent group”, Siberian Math. J., 46:3 (2005), 527–534  mathnet  crossref  mathscinet  zmath  isi
    2. E. G. Kukina, “The averaged Dehn function relative to a given probability measure”, Siberian Math. J., 47:2 (2006), 298–300  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Roman'kov, “Asymptotic growth of averaged Dehn functions for nilpotent groups”, Algebra and Logic, 46:1 (2007), 37–45  mathnet  crossref  mathscinet  zmath  isi
    4. Young R., “Averaged Dehn functions for nilpotent groups”, Topology, 47:5 (2008), 351–367  crossref  mathscinet  zmath  isi  elib  scopus
    5. Bogopolski O., Ventura E., “The mean Dehn functions of abelian groups”, Journal of Group Theory, 11:4 (2008), 569–586  crossref  mathscinet  zmath  isi  scopus
    6. Gilman R., Miasnikov A., Osin D., “Exponentially Generic Subsets of Groups”, Illinois J Math, 54:1 (2010), 371–388  mathscinet  zmath  isi  elib
    7. Gilman R.H., Myasnikov A., Roman'kov V., “Random equations in nilpotent groups”, J Algebra, 352:1 (2012), 192–214  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. V. Men'shov, “Random systems of equations in free abelian groups”, Siberian Math. J., 55:3 (2014), 440–450  mathnet  crossref  mathscinet  isi  elib  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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